What the wrong with this proof

[maw26]

F (n): (for all a, b €N) (max (a, b) =n --> a=b)

Where max (a, b) is the maximum of the two numbers a, b
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1st
F (0)
Max (a, b) = 0 then a≤0 and b≤0 so a=0 and b=0 a=b so F (0) true
Then
Suppose F (K) is true
Let max (a, b) = K+1 then max (a-1, b-1) =k
So a-1=b-1.however, this implies a-1+1=b-1+1, i.e. a=b
By the induction we proof that F (n) is true for all n € N

 

[LCKurtz]

I don't understand what you are trying to prove. Please give the exact statement of the problem.

 

[maw26]

is this statement true or false (use proof by induction)
F (n): (for all a, b €N) (max (a, b) = n --> a=b)


is the proof right

 

[LCKurtz]

I suggest you try to state what you are trying to prove as a simple English sentence. Notice that part of the actual statement of the problem is to decide whether the statement is true or false.